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Kantowski-Sachs Universe in the Varying Speed of Light Theory

In this work we consider the Kantowski-Sachs (KS) universe in the framework of varying speed of light theory. We present the general solutions of the gravitational field equations with variable speed of light $c(t)$, gravitational coupling parameter $G(t)$ and the decaying vacuum energy $Λ(t)$ for the KS model. In the limiting case for the equation of state (EOS) parameter $γ=2$ (stiff fluid with $p=ρc^2$) and $γ=1$ (dust with $p=0$), exact solutions of the field equations are obtained. The numerical solutions are also presented for both the cases. Moreover, it is shown that in the limiting case of large time, the mean anisotropy parameter tends to zero for $γ=2$ and $γ=1$. Thus the time variation of the fundamental constants provides an effective mechanism for the isotropization of the KS universe.